What is the derivative of 4x^3e^x ?

The derivative of 4x^3e^x is 4(3x^2e^x+e^xx^3)

What is the first derivative of 4x^3e^x ?

The first derivative of 4x^3e^x is 4(3x^2e^x+e^xx^3)

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\frac{d}{d x} (4 x^{3} e^{x})

4 (3 x^{2} e^{x} + e^{x} x^{3})

Solution steps

\frac{d}{d x} (4 x^{3} e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{3} e^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = e^{x}

= 4 (\frac{d}{d x} (x^{3}) e^{x} + \frac{d}{d x} (e^{x}) x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (e^{x}) = e^{x}

= 4 (3 x^{2} e^{x} + e^{x} x^{3})

x \to - \infty lim (- 4 x)

\frac{\partial}{\partial x} (x^{2} y)

\frac{d}{d x} ((e^{2 x})^{s e c (x)})

f (t) = 2 sin (t)

f (x) = \frac{3 - 2 x}{3 + 2 x}

What is the derivative of 4x^3e^x ?
The derivative of 4x^3e^x is 4(3x^2e^x+e^xx^3)
What is the first derivative of 4x^3e^x ?
The first derivative of 4x^3e^x is 4(3x^2e^x+e^xx^3)